"says Paul, “is the knowledge of sin.” “I had not known sin, but by the law: for I had not known lust, except the law had said, Thou shalt not covet.” Some who labor in word and doctrine have not a practical understanding of the law of God and its holy claims, or of the atonement of Christ. They themselves need to be converted before they can convert sinners. 2T 512.1"
"Therefore by the deeds of the law there shall no flesh be justified in his sight: for by the law is the knowledge of sin."
The EGW passage directly quotes Romans 3:20, making it an explicit allusion. The context in EGW's writing reinforces the same point made in Romans: that the law reveals sin.
"The faithful mirror which would reveal the defects in the character is neglected; therefore deformity and sin exist, and are apparent to others, if not understood by those who are in fault. The hateful sin of selfishness exists to a great degree, even in some who profess to be devoted to the work of God. If they would compare their character with His requirements, especially with the great standard, His holy, just, and good law, they would ascertain, if earnest, honest searchers, that they are fearfully wanting. But some are not willing to look far enough or deep enough to see the depravity of their own hearts. They are wanting in very many respects; yet they remain in willing ignorance of their guilt, and are so intent upon caring for their own interests that God has no care for them. 2T 512.2"
"For if any be a hearer of the word, and not a doer, he is like unto a man beholding his natural face in a glass: For he beholdeth himself, and goeth his way, and straightway forgetteth what manner of man he was."
Both passages use the metaphor of a mirror to illustrate how one can see their flaws and shortcomings. James speaks of forgetting what one looks like in the mirror, while EGW speaks of neglecting the mirror and remaining ignorant of one's faults. The underlying concept of using a standard (the Word/law) to reveal imperfections is shared.